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Simplifying 11 + v + -12 = 3(1 + 5v) + 8(v + 5) Reorder the terms: 11 + -12 + v = 3(1 + 5v) + 8(v + 5) Combine like terms: 11 + -12 = -1 -1 + v = 3(1 + 5v) + 8(v + 5) -1 + v = (1 * 3 + 5v * 3) + 8(v + 5) -1 + v = (3 + 15v) + 8(v + 5) Reorder the terms: -1 + v = 3 + 15v + 8(5 + v) -1 + v = 3 + 15v + (5 * 8 + v * 8) -1 + v = 3 + 15v + (40 + 8v) Reorder the terms: -1 + v = 3 + 40 + 15v + 8v Combine like terms: 3 + 40 = 43 -1 + v = 43 + 15v + 8v Combine like terms: 15v + 8v = 23v -1 + v = 43 + 23v Solving -1 + v = 43 + 23v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-23v' to each side of the equation. -1 + v + -23v = 43 + 23v + -23v Combine like terms: v + -23v = -22v -1 + -22v = 43 + 23v + -23v Combine like terms: 23v + -23v = 0 -1 + -22v = 43 + 0 -1 + -22v = 43 Add '1' to each side of the equation. -1 + 1 + -22v = 43 + 1 Combine like terms: -1 + 1 = 0 0 + -22v = 43 + 1 -22v = 43 + 1 Combine like terms: 43 + 1 = 44 -22v = 44 Divide each side by '-22'. v = -2 Simplifying v = -2
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